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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/optimization/optimization_ex1" target="_blank">Open optimization_ex1 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example optimization_ex1:
*   example-opt -tao_monitor -tao_view -tao_type nls
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=441
    n_local_nodes()=441
  n_elem()=100
    n_local_elem()=100
    n_active_elem()=100
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "Optimization"
    Type "Optimization"
    Variables="u"
    Finite Element Types="LAGRANGE", "JACOBI_20_00"
    Infinite Element Mapping="CARTESIAN"
    Approximation Orders="SECOND", "THIRD"
    n_dofs()=441
    n_local_dofs()=441
    n_constrained_dofs()=80
    n_local_constrained_dofs()=80
    n_vectors()=4
    n_matrices()=2
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 14.8776
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 25
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 80
      Average DoF Constraint Length= 0

iter =   0, Function value: 0,  Residual: 0.217778
iter =   1, Function value: -0.281146,  Residual: 1.41941e-06
Tao Object: 1 MPI processes
  type: nls
      Rejected matrix updates: 0
      Newton steps: 1
      BFGS steps: 0
      Scaled gradient steps: 0
      Gradient steps: 0
      nls ksp atol: 0
      nls ksp rtol: 1
      nls ksp ctol: 0
      nls ksp negc: 0
      nls ksp dtol: 0
      nls ksp iter: 0
      nls ksp othr: 0
  TaoLineSearch Object:   1 MPI processes
    type: more-thuente
  KSP Object:   1 MPI processes
    type: stcg
  total KSP iterations: 28
  convergence tolerances: fatol=1e-10,   frtol=1e-10
  convergence tolerances: gatol=1e-08,   steptol=0,   gttol=0
  Residual in Function/Gradient:=1.41941e-06
  Objective value=-0.281146
  total number of iterations=1,                          (max: 50)
  total number of function evaluations=7,                  max: 128
  total number of gradient evaluations=2,                  max: 128
  total number of Hessian evaluations=1
  Solution converged:   estimated f(x)-f(X*) <= fatol
Tao optimization solver convergence/divergence reason: CONVERGED_FATOL

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 09:41:07 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.236581, Active time=0.01159                                                   |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     1          0.0000      0.000048    0.0000      0.000048    0.41     0.41     |
|   build_constraint_matrix()        100        0.0001      0.000001    0.0001      0.000001    0.74     0.74     |
|   build_sparsity()                 1          0.0004      0.000395    0.0004      0.000435    3.41     3.75     |
|   cnstrn_elem_mat_vec()            100        0.0001      0.000001    0.0001      0.000001    0.93     0.93     |
|   create_dof_constraints()         1          0.0005      0.000500    0.0010      0.001025    4.31     8.84     |
|   distribute_dofs()                1          0.0001      0.000083    0.0004      0.000434    0.72     3.74     |
|   dof_indices()                    400        0.0001      0.000000    0.0001      0.000000    1.26     1.26     |
|   enforce_constraints_exactly()    10         0.0004      0.000037    0.0004      0.000037    3.16     3.16     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0004      0.000351    0.0004      0.000351    3.03     3.03     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          1          0.0002      0.000233    0.0003      0.000283    2.01     2.44     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0014      0.001368    0.0014      0.001368    11.80    11.80    |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        140        0.0003      0.000002    0.0003      0.000002    2.72     2.72     |
|   init_shape_functions()           41         0.0000      0.000001    0.0000      0.000001    0.19     0.19     |
|   inverse_map()                    120        0.0001      0.000001    0.0001      0.000001    1.03     1.03     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             140        0.0001      0.000001    0.0001      0.000001    1.13     1.13     |
|   compute_face_map()               40         0.0001      0.000002    0.0002      0.000005    0.72     1.86     |
|   init_face_shape_functions()      40         0.0000      0.000001    0.0000      0.000001    0.19     0.19     |
|   init_reference_to_physical_map() 41         0.0002      0.000004    0.0002      0.000004    1.33     1.33     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 1          0.0003      0.000258    0.0003      0.000258    2.23     2.23     |
|   renumber_nodes_and_elem()        2          0.0000      0.000005    0.0000      0.000005    0.09     0.09     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         1          0.0000      0.000018    0.0017      0.001669    0.16     14.40    |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0001      0.000131    0.0001      0.000131    1.13     1.13     |
|                                                                                                                 |
| OptimizationSystem                                                                                              |
|   solve()                          1          0.0022      0.002184    0.0070      0.007001    18.84    60.41    |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               1          0.0000      0.000012    0.0000      0.000012    0.10     0.10     |
|                                                                                                                 |
| TaoOptimizationSolver                                                                                           |
|   gradient()                       2          0.0001      0.000040    0.0001      0.000070    0.69     1.21     |
|   hessian()                        1          0.0003      0.000297    0.0003      0.000328    2.56     2.83     |
|   objective()                      7          0.0004      0.000056    0.0007      0.000096    3.40     5.81     |
|   solve()                          1          0.0037      0.003674    0.0048      0.004817    31.70    41.56    |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            1200       0.0116                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example optimization_ex1:
*   example-opt -tao_monitor -tao_view -tao_type nls
***************************************************************
</pre>
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